Optimal control technique for magnet design in inside-out nuclear magnetic resonance

Abstract

The magnets used in a family of inside-out nuclear magnetic resonance (NMR) well-logging tools usually consist of several segments of magnet materials, with each segment magnetized differently. In a tool, the magnet is surrounded with a nonlinear magnetic material, such as ferrite or steel, that is primarily used in the RF coil or in shielding the electronic components from strong magnetic fields. The main objective of the tool design is to find a set of magnetization vectors that result in a desired magnetic field profile in a particular region. A typical nonlinear finite-element method (FEM) model of such a design has about quarter of a million unknowns and requires about 35 h of processor time on a Sun Ultra 60 296-MHz machine with 1 GB of RAM. It generally requires many executions of the nonlinear FEM to arrive at a satisfactory design. In this paper, an optimal control technique in conjunction with FEM is proposed to speed up the design process. A magnet built from the design showed excellent agreement between the measured and computed data and validated the numerical method.

Mobile single-sided NMR

“…This principle is used in mechanical shimming, but not only by incorporating additional magnets where needed, but also magnetic metal pieces. The field profiles are often optimized with the help of numerical simulations [200][201][202][203][204][205][206][207], for example, to arrive at a magnet with a maximum sensitive volume in a linear gradient field [200][201][202][203], to reduce the weight of such a magnet [201], and to arrive at a large region of homogeneous field [202]. Such optimizations can focus on identifying suitable pole caps [208,202,203] or finding proper magnet shapes and orientations.…”

An analytical methodology for magnetic field control in unilateral NMR

“…Sample measurements show the prototype instrument obtains a field homogeneity of 0.13 T/m in the sensitive volume, on par with other optimal designs of this type [2,16]. The field strength for the design presented is lower than that often used is unilateral systems such as the NMR MOUSE.…”

“…Designs can be optimized by performing successive simulations while varying parameters to minimize some goal function and this technique has previously been employed in unilateral magnet design [16]. The drawback of this approach is that specific parameters (e.g., size, position, and strength of magnets) must be selected for the optimization and the parameter space must be empirically selected to suit the desired magnet topology.…”

Least Squares Magnetic-Field Optimization for Portable Nuclear Magnetic Resonance Magnet Design

“…Our approach is unique in comparison to other magnet optimization techniques [8], [30]- [34] in that it combines a target field optimization that locates a global optimum with a few simple matrix calculations to the design of adjustable permanent magnet assemblies. Other linear programing based techniques like lpnorm [30], [31] have been applied to coil designs and could provide an alternative optimization technique within our implementation strategy.…”